Grandfather Laino is getting ready once again to visit another of his dream places, Jujuy.
He already has his suitcase packed and has put on its combination lock, which consists of $$$N$$$ dials, each of which contains the digits from $$$0$$$ to $$$8$$$ in order.
The lock can only be opened when the correct code is entered, and for that each dial has to show the correct number.
If at some moment a dial shows digit $$$d$$$ and we turn it to the right, it changes to digit $$$d+1$$$, except when it shows digit $$$8$$$, in which case it changes to $$$0$$$. Similarly, if a dial shows digit $$$d$$$ and we turn it to the left, it changes to digit $$$d-1$$$, except when it shows digit $$$0$$$, in which case it changes to $$$8$$$.
Grandfather Laino had set the combination, and to lock the suitcase again he wanted to bring it to the combination with all zeros, so as not to reveal his true code. To achieve this, if a dial showed digit $$$d$$$, he had to turn it $$$d$$$ times to the left. Since Grandfather Laino confuses left with right, he turned it $$$d$$$ times to the right instead.
When he arrived at the airport, he weighed his suitcase and got a surprise. The suitcase exceeded the maximum allowed weight, so he had to open it to remove some objects. Unfortunately, he forgot the lock combination, but his confusion when turning the dials can help him reconstruct it.
Could you help Grandfather by telling him what his combination was, seeing only how the lock looks after Laino turned the dials?
The first line contains an integer $$$N$$$ ($$$1 \leq N \leq 100$$$), the number of dials of the lock.
The second line contains $$$N$$$ digits $$$R_1, R_2, \dots, R_N$$$ ($$$0 \leq R_i \leq 8$$$), where $$$R_i$$$ is the digit shown by the $$$i$$$-th dial. It is guaranteed that at least one of the digits is different from $$$0$$$.
A line with $$$N$$$ digits, which form Grandfather Laino's initial combination.
It can be shown that there is a unique valid initial combination.
42 0 2 6
1 0 1 3
33 8 8
6 4 4
In the first example, Laino's code is 1 0 1 3. On the first dial, instead of turning it once to the left, he turned it to the right, and that is why it showed a $$$2$$$. The same happened with the third dial. On the second dial, since it had a zero he should not have turned it and it stayed as it was. The fourth dial had a $$$3$$$, so he should have turned it $$$3$$$ times to the left, but he turned it $$$3$$$ times to the right, showing a $$$6$$$.
